NDLI: Synthesis of Cucker-Smale type flocking via Mean Field stochastic control theory: Nash equilibria

Content Provider	IEEE Xplore Digital Library
Author	Nourian, M. Caines, P.E. Malhame, R.P.
Copyright Year	2010
Description	Author affiliation: CIM, Department of Electrical & Computer Engineering, McGill University, 3480 University Street, Montreal, QC H3A 2A7, Canada (Nourian, M.; Caines, P.E.) \|\| GERAD, Montreal and Department of Electrical Engineering, École Polytechnique de Montréal, QC H3C 3A7, Canada (Malhame, R.P.)
Abstract	In this paper we study a controlled flocking model, where the state of each agent consists of both its position and its controlled velocity, by use of Mean Field (MF) stochastic control framework. We formulate large population stochastic flocking problem as a dynamic game problem in which the agents have similar dynamics and are coupled via their nonlinear individual cost functions. These cost functions are based on the Cucker-Smale (C-S) flocking algorithm in its original uncontrolled formulation. For this nonlinear dynamic game problem we derive a set of coupled deterministic equations approximating the stochastic system of agents as the population goes to infinity. Subject to the existence of a unique solution to this system of equations, the set of MF control laws for the system possesses an εN-Nash equilibrium property, where εN → 0 as the population size, N, goes to infinity. Hence, this model may be regarded as a controlled game theoretic formulation of the C-S flocking model in which each agent, instead of responding to an ad-hoc algorithm, obtains its control law from a game theoretic Nash equilibrium. Moreover, we retrieve the MF Linear-Quadratic-Gaussian (LQG) dynamic game solution for the C-S algorithm from the general nonlinear MF system of equations.
Starting Page	814
Ending Page	819
File Size	424883
Page Count	6
File Format	PDF
ISBN	9781424482153
e-ISBN	9781424482160
DOI	10.1109/ALLERTON.2010.5706992
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-09-29
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Biological system modeling Heuristic algorithms Stochastic processes Games Cost function Mathematical model Equations
Content Type	Text
Resource Type	Article

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